Right now it's like the extrusion bounds are going through the center of the texture's edge, when it needs to extend all the way to the inside edge of the texture's edge.

The two could line up exactly if they were using the same points defining the curve and were rasterized at the same resolution, but clearly that's not the case. Your only choice is to ensure the extrusion covers up the lower-res texture edge by simply extruding that side more.